hw 8 - rhodes (ajr2283) HW08 Gilbert (56380) This print-out...

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rhodes (ajr2283) – HW08 – Gilbert – (56380) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Which, iF any, oF the Following A. −−→ QP , B. PQ, are representations oF vectors when P, Q are points in 3-space? 1. both oF them 2. A only correct 3. neither oF them 4. B only Explanation: A. TRUE: −−→ QP is the displacement vector having initial point P and terminal point Q . B. ±ALSE: PQ is the line segment from P to Q . keywords: vectors, scalars, T/±, line segment, displacement vector, length 002 10.0 points ±ind the vector v having a representation by the directed line segment −−→ AB with respect to points A (3 , 2) and B ( 2 , 1). 1. v = a− 1 , 1 A 2. v = a− 5 , 3 A 3. v = a 5 , 3 A 4. v = a− 5 , 3 A correct 5. v = a 1 , 1 A 6. v = a 1 , 1 A Explanation: Since −−→ AB = a− 2 3 , 1 + 2 A , we see that v = a− 5 , 3 A . 003 10.0 points When u , v are the displacement vectors u = −→ AP , v = −→ AC , determined by the parallelogram A B C P Q R S O express −−→ QC in terms oF u and v . 1. −−→ QC = 1 2 u + v 2. −−→ QC = 1 2 u v 3. −−→ QC = u + 1 2 v 4. −−→ QC = 1 2 v 5. −−→ QC = 1 2 u 6. −−→ QC = 1 2 v u correct Explanation: By the parallelogram law For the addition oF vectors we see that −−→ QC = 1 2 v u .
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rhodes (ajr2283) – HW08 – Gilbert – (56380) 2 004 10.0 points Determine a so that the vector u = a− 11 , 4 A is a linear combination u = a v + b w of vectors v = a 3 , 1 A , w = a 2 , 1 A . 1. a = 2 2. a = 3 correct 3. a = 2 4. a = 1 5. a = 3 Explanation: Since addition and scalar multiplication of vectors is carried out componentwise, we see that u = a− 11 , 4 A = a a 3 , 1 A + b a 2 , 1 A = a 3 a + 2 b, a + b A . Thus 3 a + 2 b = 11 , a + b = 4 . Consequently, after solving these for a we see that a = 3 . keywords: vectors, vector sum, linear combi-
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hw 8 - rhodes (ajr2283) HW08 Gilbert (56380) This print-out...

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